I already mentioned I wouldn’t mind a guy babysitting as long as he’s mature enough. My fiance babysits his nieces and nephews whenever he is around. My brother used to babysit our younger siblings. I have never heard from from anyone that a man can’t babysit.
If God intended women to stay at home, he wouldn’t have made them capable of working and blessed them with intellect. But as it turns out, women are equally capable of working and earning.